let X be non empty set ; :: thesis: for f being PartFunc of X,REAL holds
( max+ f is nonnegative & max- f is nonnegative )
let f be PartFunc of X,REAL; :: thesis: ( max+ f is nonnegative & max- f is nonnegative )
for x being object st x in dom (max+ f) holds
0 <= (max+ f) . x by RFUNCT_3:37;
hence max+ f is nonnegative by Th52; :: thesis: max- f is nonnegative
for x being object st x in dom (max- f) holds
0 <= (max- f) . x by RFUNCT_3:40;
hence max- f is nonnegative by Th52; :: thesis: verum